Problem: $f(x) = -4x^{2}+3$ What is the range of $f(x)$ ?
Consider the range of $-4x^{2}$ The range of $x^2$ is $\{\, y \mid y \ge 0 \,\}$ Multiplying by $-4$ flips the range to $\{\, y \mid y \le 0 \,\}$ To get $-4x^{2}+3$, we add $3$.